Implications of placing a porous block in a mixed-convection heat-transfer, lid-driven cavity heated from below

The current numerical study investigates the characteristics of an incompressible laminar, mixed-convection heat transfer in a square lid-driven cavity in the presence of a porous block. The cavity consists of two adiabatic vertical boundaries, a cold top lid that is sliding rightward at a constant speed, and a heated bottom boundary. The governing transport equations within the porous media were treated according to the volume-average theory, while Navier-Stokes equations were employed to represent the transport phenomena in the rest of the cavity. Further, the governing equations were solved using a finite element formulation based on the Galerkin method of weighted residuals. Comparisons of streamlines, isotherms, and average Nusselt number were exhibited to show the impact of the Richardson number, porous block size, and location on the transport phenomena within the cavity. The increase of Richardson number brings about an appreciated increase in natural convection effects, which enhances flow mixing and heat-transfer rate. Moreover, the presence of the porous block results in an appreciated increase in Nusselt number when compared against the case with no block, especially for Ri ≈ 1. What is more, the considered blockage ratios of 0.125, 0.25, and 0.5 show close Nusselt number predictions between the two aforementioned cases. It was interesting to notice that the latter third case falls considerably behind in Nusselt number predictions for Ri < 1 but it surpasses them when Ri exceeds 7. Finally, the optimal heattransfer results were obtained when placing the porous block at the center of the cavity for Ri ≤ 1 while placing it at the bottom section rendered the same objective for Ri > 1.